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The strict inequality conjecture for critical and unification probabilities on non-amenable graphs
Strict inequality conjecture. If $\Gamma$ is non-amenable and quasi-transitive, then
openinfinite-clusters non-amenable-graphs percolation
07
Non-amenability conjecture for traces of branching random walks
Non-amenability conjecture. Let $\mu$ be the measure of the trace of a transient BRW on a URG. Then $\mu$ is non-amenable.
openbranching-random-walks non-amenable-graphs unimodular-random-graphs
04